Express the integral U f(x, y, z) dV as an iterated integral in six different ways, where E is the solid bounded by the given surfaces. Jo y=x², z = 0, J-√16-42 y + 4z = 16 I√5 I-V f(x, y, z) dz dy dx f(x, y, z) dz dx dy f(x, y, z) dx dz dy f(x, y, z) dx dy dz f(x, y, z) dy dz dx f(x, y, z) dy dx dz

Q: (E) Every integral | f dA where R is a rectangle in the xy-plane can be F AiS E R d b expressed as…

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Q: Apply Green's Theorem to evaluate the integral (6y² dx + 6x² dy), where C is the triangle bounded by…

A: Our objective is given below:

Q: Verify Green theorem for the line integral f (x³ -x²y) dx + xy² dy 6x where C is the boundary of the…

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Q: = [ry, yz, cz] and C is 6- Evaluate the line integral fc F dr, where F e boundary of the hemisphere…

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Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

Q: Evaluate (x + y)ds where C is the straight-line segment x=t, y = (4 – t), z = 0 from (0,4,0) to…

A: We have to find the given line integral.

Q: Use Green's theorem to evaluate the line integral frdx + (a - 20)dy where C is the boundary of the…

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Q: Integrate G(x,y,z)=z-x over the portion of the graph of z=x+3y² that lies above the triangle in the…

A: Given that G  x, y, z  = z - x              The portion of the graph a curve z = x + 3y2 above…

Q: Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 -…

A: We have to evaluate the integral ∬S2xyi^−yzj^+zxk^⋅dS where S is the path of the paraboloid…

Q: Houble integral dA R ne parallelogram in the xy-plane bounded by c + y = 0 and x + y = 2. Use the…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-4*…

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Q: F(x, y, z) = (2xe*) i+ (2y + 3y?22)j+ (x²e* + 2y³z) k is conservative. Find a functionf such that F…

A: To find the function f  And then evaluate the line integral along the given curve.

Q: Evaluate the triple integral of f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball æ? + y² +…

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Q: If a(0, –1, 3) + b(1, 1, 1) – c(1, 2, 5) = (-2, 3, –8), determine a, b and c.

A: If a0,-1,3+b1,1,1-c1,2,5=-2,3,-8determibe a,b,c

Q: Use cylindrical coordinates to calculate the triple integral [ f(x, y, z) dV for the function f(x,…

A: Given that the function is                              f(x, y, z)=11156zx2+y2, and the region…

Q: 5) Evaluate x² +1 4x³ + 12x dx

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Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= 7 x° + y curl F=i z

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Q: Find the area of the surface defined by x + y + z = 1, x2 + 2y2 ≤ 1.

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Q: Evaluate the triple integral of f(x,y, z) z(x2 + y? + z²)-3/2 over the part of the ball x² + y² + z²…

A: please  see the next step for solution

Q: Let R be the region in the ry-plane such that /| f(z, y) dA = |(2, y) dy de + | f(x,y) dy dx, (x-2)2…

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Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: Evaluate the line integral [F.dr where Y F(x, y, z) = (x + yz, x + z, xy) and y: line segment from…

A: The given problem is evaluate the given line integral of given vector field F over the given path of…

Q: F = (y³, –a³, xyz). Find V x F. Let S be the surface parametrized by F(u, v) = (cos(u), sin(u), v)…

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Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: Set up an integral for the circulation of F along the curve C, where F = (x² + y², x² - y²) and C is…

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